Section 4: Soil and Water Conservation Engineering
Surveying: Distance, Angles & Traversing
Subtopic: Traverse closing error magnitude
Question Statement:
In a closed traverse survey, the sum of latitudes is $\sum L = 0.40\text{ m}$ and the sum of departures is $\sum D = -0.40\text{ m}$. The total linear closing error is ________ $\text{m}$ (round off to two decimal places).
Answer Key:
0.57
Step-by-Step Solution & Explanation
The linear closing error $e$ is given by:
$e = \sqrt{(\sum L)^2 + (\sum D)^2}$
Substituting $\sum L = 0.40\text{ m}$ and $\sum D = -0.40\text{ m}$:
$e = \sqrt{0.40^2 + (-0.40)^2} = \sqrt{0.1600 + 0.1600} = \sqrt{0.3200} = 0.566\text{ m}$
Rounding to two decimal places: $0.57\text{ m}$.